5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

Essential Question: Describe the shape of the graph of a quadratic function and basic properties of the graph

FOIL FOIL is an acronym for “First, Outer, Inner, Last”

Multiply the indicated terms together Combine like terms

Example: y = (2x + 3)(x – 4)

y = (2x + 3)(x – 4)

FirstLast

Inner

Outer

First: 2x • x = 2x2

Outer: 2x • -4 = -8xInner: 3 • x = 3xLast: 3 • -4 = -12

y = 2x2 – 8x + 3x – 12y = 2x2 – 5x - 12

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

A quadratic function is a function that can be written in the standard form: f(x) = ax2 + bx + c, where a ≠ 0 The term which uses x2 is called the quadratic term The term which uses x is called the linear term The term without an x next to it is called the constant

term

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

Example 1: Classifying Functions Determine whether each function is linear or

quadratic. Identify the quadratic, linear, and constant terms.

y = (2x + 3)(x – 4)

f(x) = 3(x2 – 2x) – 3(x2 – 2)

y = 2x2 – 5x – 12Quadratic Term: 2x2

Linear Term: -5xConstant Term: -12

f(x) = -6x + 6Linear Term: -6xConstant Term: 6

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

The graph of a quadratic function is a parabola. Parabola’s are ‘U’-shaped.

The axis of symmetry is the line that divides a parabola in half.

The vertex of a parabola is the point at which the parabola intersects the axis of symmetry. The y-value of the vertex represents the

maximum (or minimum) value of the function

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

Below is a graph of f(x) = 2x2 – 8x + 8. Identify the vertex, axis of symmetry, points

P’ and Q’ corresponding to P and Q

P

Q

1 2 3 4 5 6 7 8 9–1 x

1

2

3

4

5

6

7

8

9

–1

y

Vertex is at (2, 0)

Axis of symmetry is: x = 2P’ = (3, 2)Q’ = (4, 8)

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

Your Turn Identify the vertex, axis of symmetry, points

P’ and Q’ corresponding to P and QVertex is at (1, -1)

Axis of symmetry is: x = 1P’ = (3, 3)Q’ = (0, 0)

P

Q1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS

Assignment Page 241 Problems 1 – 15 (all problems)